A wire of resistance R is folded thrice on itself.It's resistance will become:
(a)R/16
(b)16R
(c)R/64
Answers
Answer:
R/64.
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Answer:
If a metallic wire has length L, diameter d and material of electrical resistivity rho, the resistance R of a wire is inversely proportional to the cross section A of the wire,
R = rho L / A
being
A = π d^2 / 4
Assuming that the wire is always used with the same length (L), the variation of the diameter (d) will cause a variation in the electrical resistance (R). So we are talking about its electrical resistance per unit length.
IN THIS CASE it could be said that if the diameter is reduced by half (d/2) , the area of the cross section is reduced four times (A/4) and then, the resistance would increase four times, i.e., the new resistance will be 4R . . . right?
WRONG ! There is something more, something very important.
The process to reduce the diameter is called "drawing" (“trefilado”, in Spanish), which in this case corresponds to a cold work of 75% (% CW = 75), which is a huge change which produces a lot deformation in the grains of the polycrystalline material that composes the conductor. This large number of deformation defects greatly increases the electrical resistivity rho of the material, and therefore, the answer to the question is
THE NEW RESISTANCE WILL BE GREATER THAN 4R,
and we can´t know how much greater the resistance can be, without having more detailed information about the microstructure and composition of the material.